17O solid-state NMR spectroscopy of A2B2O7 oxides: quantitative isotopic enrichment and spectral acquisition?

The potential of 17O NMR spectroscopy for the investigation of A2B2O7 ceramic oxides important in the encapsulation of radioactive waste is demonstrated, with post-synthetic enrichment by exchange with 17O2 gas. For Y2Sn2O7, Y2Ti2O7 and La2Sn2O7 pyrochlores, enrichment of the two distinct O species is clearly non quantitative at lower temperatures (∼700 °C and below) and at shorter times, despite these being used in prior work, with preferential enrichment of OA2B2 favoured over that of OA4. At higher temperatures, the 17O NMR spectra suggest that quantitative enrichment has been achieved, but the integrated signal intensities do not reflect the crystallographic 1 : 6 (O1 : O2) ratio until corrected for differences in T1 relaxation rates and, more importantly, the contribution of the satellite transitions. 17O NMR spectra of Y2Zr2O7 and Y2Hf2O7 defect fluorites showed little difference with any variation in enrichment temperature or time, although an increase in the absolute level of enrichment (up to ∼7.5%) was observed at higher temperature. DFT calculations show that the six distinct resonances observed cannot be assigned unambiguously, as each has contributions from more than one of the five possible next nearest neighbour environments. For La2Ti2O7, which adopts a layered perovskite-like structure, little difference in the spectral intensities is observed with enrichment time or temperature, although the highest absolute levels of enrichment (∼13%) were obtained at higher temperature. This work demonstrates that 17O NMR has the potential to be a powerful probe of local structure and disorder in oxides, but that considerable care must be taken both in choosing the conditions for 17O enrichment and the experimental acquisition parameters if the necessary quantitative measurements are to be obtained for more complex systems.


S4
.5 Typical experimental powder XRD pattern for a synthesised sample of Y 2 Hf 2 O 7 and powder pattern simulated from literature data (ICSD 153819). Peak intensities are normalised relative to the 111 peak. Figure S1.6 Typical experimental powder XRD pattern for a synthesised sample of La 2 Ti 2 O 7 and powder pattern simulated from literature data (ICSD 1950). Peak intensities are normalised relative to the peak at ~ 30° 2θ. Figure S1.7 SEM images of powdered samples of (a) Y 2 Sn 2 O 7 , (b) Y 2 Ti 2 O 7 , (c) La 2 Sn 2 O 7 , (d) Y 2 Zr 2 O 7 , (e) Y 2 Hf 2 O 7 and (f) La 2 Ti 2 O 7 .

Mass Spectrometry
Samples were studied using mass spectrometry, as described in the main text. Results are reported below as counts per isotope, with the instrumental standard error of the mean per measurement.   Figure S3.1a plots δ iso exp against σ iso calc for all structures and shows a good linear correlation (R 2 = 0.9786). This was the procedure used to reference the calculations in the main text. However, the gradient of the line of best fit is not exactly equal to -1 (as would be expected for an ideal case), suggesting that the DFT calculations have a tendency to slightly overestimate any shielding differences. In this case a calculated shift value is produced using where c and m are the intercept and slope, respectively, from linear regression. In the ideal case, where m = 1, Eqn. S3.2 then simplifies to Eqn. S3.1 and c = σ ref .
As shown in Figure S3.1b, a slightly better correlation (R 2 = 0.9896) is obtained if some of the simple oxides in Table S3.1 are not included in the analysis (those shown in red). Many of these compounds contain heavier nuclei (i.e., those that might be more affected by relativity, which is only included in the ZORA approximation). It should also be noted that previous work has shown that the failure of GGA PBE to treat the unoccupied Ca 3d states correctly led to significant errors in the 17 O chemical shifts and CaO and calcium aluminosilicates. S1 Calculations on the compounds highlighted in Table   S3.1 may also suffer from similar problems. However, it should be noted that this results in a change to both m (now 0.9002) and c (now 228.808), leading to shielding values that can differ by 5-7 ppm at the extreme of the shielding range. This level of uncertainty may have relevance when attempting to assign some of the spectra discussed in the main text and suggests that the accuracy of the calculated values should always be treated with some caution. The equation given in Figure S3.1b was chosen to reference the calculations in the first parts of the main text.  S9-11 184.78 64 S9-11 187.57 61 S9-11 β-Mg 2 SiO 4 S12 214.38 38 S11,S13

S4. 17 O slow MAS spectra
Although, in principle, a C Q value of zero is expected for O1 in ideal pyrochlore materials, spinning sidebands resulting from satellite transitions (ST) are observed in experimental spectra, indicating a small but non-zero magnitude for this interaction. The magnitude of the coupling constant can be estimated by fitting the sideband manifold in spectra acquired at slow (i.e., 3.25, 3.6 and 6.5 kHz) MAS rates, as shown in Figure S4.1. 6.5 kHz MAS. Spinning sidebands resulting from O2 are marked *.

S5. NMR of La 2 Sn 2 O 7
The O1 resonance in La 2 Sn 2 O 7 exhibits a complex multiplet lineshape as a result of couplings to four 139 La neighbours. The lineshape is affected both by J couplings (constant value in Hz with field) and a quadrupolar-dipolar cross term (a second-order interaction that survives MAS). S43-S44 Figure S5.1 shows the variation in this lineshape as a function of B 0 field strength. frequency-stepped wideline CPMG spectrum shown in Figure S5.2. This fitting assumed the effect of the CSA on the broad quadrupolar lineshape to be negligible. This is supported by the spectra in Figure S5.3, simulated with and without the CSA included, using the NMR parameters predicted by DFT calculations. Given a O-La distance of 2.317 Å, this leads to estimates of the cross term between ~50 Hz at 9.4 T to ~20 Hz at 20.0 T. This is of a similar magnitude to the J coupling (predicted by DFT calculations to be ~30 Hz), leading to the complex multiplet patterns seen. Although some variation with field is observed (confirming the cross term is significant), the resolution is not sufficient to fit the lineshape or experimentally determine the couplings involved.   Figure 4 of the main text.

S8. Overall levels of 17 O enrichment
It is difficult to accurately compare the absolute levels of enrichment achieved for samples enriched under different conditions, owing primarily to the variation in the amount of gas used in each enrichment experiment, and also to differences in the masses of the sample studied and in the microstructure and grain size of (i) different pyrochlores and (ii) different batches (i.e., synthesised at different times) of the same pyrochlore. (Note SEM images are shown in Section S1). While it is not easy to estimate the experimental uncertainty this produces in any one measurement, it is possible to consider the overall trends in absolute enrichment level (with varying time and temperature). Figure S8. obtained for 96 h heating also appear to be lower than expected, again owing to a problem with the amount of gas used in the enrichment process.      As described in the main text, for a "unit cell" of similar size to that of a pyrochlore (i.e., containing 32 cation sites (occupied by 16 Y and 16 Zr/Hf) and 64 anion sites (occupied by 56 oxygens and 8 vacancies), there ~2.64 × 10 18 possible defect fluorite structures (resulting from ~600 million possible cation arrangements and ~4.4 billion possible anion arrangements). Even when restricting this to symmetry-unique environments it is clearly unfeasible to consider all of these (or even any statistically-relevant subset).
A set of 30 Y 2 Zr 2 O 7 defect fluorite structural models was produced, starting from a 2 × 2 × 2 supercell of ideal AO 2 fluorite. Using a FORTRAN script, 16 of the 32 cation sites were randomly selected to be occupied by Y, with the remainder occupied by Zr.
Similarly, 8 of the 64 anion sites were randomly selected to be vacant (and the remaining 56 occupied by O). The structures were geometry optimised using DFT. (It should be noted that many of these structural models were far from equilibrium and required the geometry optimisation to be carried out in two different stages; the first using the EDFT SCF solver in CASTEP for a maximum of 50 optimisation steps, and the second taking the output from the first calculation and using the DM SCF solver for up to 400 optimisation iterations). The duration of the first optimisation step was typically ~35 h (on 224 cores), the second typically ~120 h (on 64 cores). NMR parameters were then calculated (taking typically ~7 h on 64 cores). In addition, a further 4 structural models were considered. The first was a Y 2 Zr 2 O 7 pyrochlore structure (i.e., with ordering of cations and anions) generated by atom substitution from a structural model of Y 2 Sn 2 O 7 . Two models were generated from this; one by moving one 8a O to a vacant 8b site (creating a sevencoordinate Y species and an OZr 4 environment), and a second by moving another 8a O from around the same Y to a vacant 8b site (creating a six-coordinate Y species). The final structural model was a reverse pyrochlore structure, i.e., containing Y on the B site and Zr on the A site. All structures were geometry optimised using only the second optimisation procedure described above. For Y 2 Hf 2 O 7 , 30 defect fluorite models were obtained by substituting Zr for Hf in the structures described above and subjecting these to further S31 geometry optimisation. The four corresponding Hf-containing pyrochlore structures were generated once more from Y 2 Sn 2 O 7 .
The structural models produced span an energy range of 5.35 eV for Y 2 Zr 2 O 7 and 5.42 eV for Y 2 Hf 2 O 7 , and five-, six-, seven-and eight-coordinate Y species are present. For Y 2 Zr 2 O 7 , the ordered pyrochlore structure was 0.41 eV higher in enthalpy than the lowest disorder structure (note, this does not take into account any contribution from configurational entropy). The structures produced by moving one and two 8a O species were 1.94 and 5.12 eV higher in energy, respectively, and the reverse pyrochlore 22.14 eV higher than the lowest energy structural model. This confirms the preference (also seen in the 89 Y NMR spectra) for Y to have a higher coordination number. The lowest energy structure produced had 2 six-coordinate, 12 seven-coordinate and 2 eight-coordinate Y species. The 17 O chemical shifts predicted from these structural models are shown in Figure S10.1a and calculated absolute C Q values in Figure S10.1a. All are very similar and small, suggesting quadrupolar broadening has a limited effect in the experimental spectrum. For Y 2 Hf 2 O 7 , the disordered structural model with the lowest energy had 1 sixcoordinate, 13 seven-coordinate and 2 eight-coordinate Y species. Interestingly, this model was higher in energy (by 1.01 eV) than the ordered pyrochlore structure. Structures produced by moving one and two 8a O species were 1.00 and 4.70 eV higher in energy, and the reverse pyrochlore 23.37 eV higher than the lowest energy structural model. This suggests a stronger preference for higher Y coordination numbers in hafnate-based materials than in the corresponding zirconate structures. The 17 O chemical shifts predicted from these structural models are shown in Figure S10.1b, and the calculated absolute C Q values in Figure S10.2b.

S12. DFT calculations for La 2 Ti 2 O 7
DFT calculations were carried out for the monoclinic and orthorhombic structural models of La 2 Ti 2 O 7 . When the referencing (and scaling) procedure outlined in Section S3 was applied, poor agreement with experiment was observed. Figure S12.1 shows the plot of calculated isotropic shieldings (σ iso calc ) and experimental isotropic shifts (δ iso exp ) shown previously in Figure S3.1a, but with the 14 points for (monoclinic) La 2 Ti 2 O 7 also added (in red it does not seem sensible to include these points in any determination of reference value and/or and scaling factor, but to facilitate comparison with experiment (and interpretation of the experimental spectra), DFT calculations were referenced using only the peaks seen in the experimental spectrum. The reference value and scaling factor were determined using the peaks at highest and lowest shift only (thereby removing any uncertainty over spectral assignment in the more crowded regions of the spectrum).
S37 Figure S12.1 Plot of δ iso exp against σ iso calc for shown previously in Figure S3.1a, with points for (monoclinic) La 2 Ti 2 O 7 added in red.  Figure   S12.2 shows the position of each type of O species within the structure of the two structural models.  S40 Figure S12.3 plots calculated NMR parameters (δ iso calc and C Q calc ) for the monoclinic and orthorhombic structural models of La 2 Ti 2 O 7 , along with the 17 O MAS NMR spectrum of La 2 Ti 2 O 7 enriched at 900 °C for 12 h. There is very little difference between the calculated parameters for the two structures, and both exhibit similar agreement with experiment, suggesting that 17 O NMR is not able to distinguish the two unambiguously.
The energy (after optimisation) of the monoclinic form was very slightly lower (by 0.44 meV) than that of the orthorhombic form. This is in agreement with the conclusion reached by Fernandes et al. S48 in previous work studying Sn-substituted La 2 Ti 2 O 7 .